Simplify the following expression: $\dfrac{8r^2}{4r^2}$ You can assume $r \neq 0$.
Explanation: $ \dfrac{8r^2}{4r^2} = \dfrac{8}{4} \cdot \dfrac{r^2}{r^2} $ To simplify $\frac{8}{4}$ , find the greatest common factor (GCD) of $8$ and $4$ $8 = 2 \cdot 2 \cdot 2$ $4 = 2 \cdot 2$ $ \mbox{GCD}(8, 4) = 2 \cdot 2 = 4 $ $ \dfrac{8}{4} \cdot \dfrac{r^2}{r^2} = \dfrac{4 \cdot 2}{4 \cdot 1} \cdot \dfrac{r^2}{r^2} $ $\phantom{ \dfrac{8}{4} \cdot \dfrac{2}{2}} = 2 \cdot \dfrac{r^2}{r^2} $ $ \dfrac{r^2}{r^2} = \dfrac{r \cdot r}{r \cdot r} = 1 $ $ 2 \cdot 1 = 2 $